Question

shown below Q1 Q2 23 24 Q6 Q7 b. The nall and altermative hypotheses for The p-valuc is Round to 4 decimal places c. Use a level of significance of α-0.05 to state the coeclusion ofth' hypothesis test in the context ofthe study. There is statistically significant evidence to conclude that a person who watches fewer movies will read fewer books than a person who watches fewer movies There is statistically significant evidence so conctude that there is a correlation between the number of movies wanched per year and the number of books read per year. Thus the regression line is useful (Round to two decimal places) reduced by 57%. 57% of all people watch about the same number ofmwes asthey Pead books each year. 2 6 8 5 reduced by 57% t The (Please round your anwer to the neaeest whole nmbor g. Use the model to predict the of books read per year for someone who watches 4 movies per year Books per year (Please round your answer to the nearest whole number.) h. Imerpret the slope of the regression line in the context of the question The slope has no practical meaning since people cannot read a negative number of books. As x goes up, y goes down i. Interpret the y-intercept in the context of the question: The average number of books read per year is predicted to be 13 books The y-intercept has no practical meaning for this study. If someone watches 0 movies per year, then that person will rcad 13 books this year Hint: Helpful Video on the Linear Regression LineG Helpéal Video on Helpful Video on Hypothesis Tests for Correlation& Textbook Pages Hints G Search or type URL 8 9 5 6

Answer 1

X	Y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
7	5	6.950	25.000	-13.182
10	5	31.769	25.000	-28.182
2	14	5.587	16.000	-9.455
0	15	19.041	25.000	-21.818
4	8	0.132	4.000	0.727
7	11	6.950	1.000	2.636
9	9	21.496	1.000	-4.636
1	14	11.314	16.000	-13.455
7	8	6.950	4.000	-5.273
0	11	19.041	1.000	-4.364
1	10	11.314	0.000	0.000

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	48	110	140.545	118.0	-97
mean	4.36	10.00	SSxx	SSyy	SSxy

sample size ,   n =   11          
here, x̅ =   4.36   ,   ȳ =   10.00  
                  
SSxx =    Σ(x-x̅)² =    140.55          
SSxy=   Σ(x-x̅)(y-ȳ) =   -97.0          

a)

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   -0.75

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b)

Ho:   ρ = 0  
Ha:   ρ ╪ 0  
n=   11  
alpha,α =    0.05  

correlation , r=   -0.7532  
t-test statistic =    t = r*√(n-2)/√(1-r²) =    -3.43535
p-value =    0.0074

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c)

option c)

d)

r²= -0.7532² =0.57

e)

option b)

f)

slope ,    ß1 = SSxy/SSxx =   -0.69017          
                  
intercept,   ß0 = y̅-ß1* x̄ =   13.01164          
                  
so, regression line is   Ŷ =   13.01   +   -0.69 *x

g)

Ŷ =   13.01   +   -0.69 * x

Ŷ =   13.01   +   -0.69 * 4 = 10(answer)

h)

option b)

i)

option d)